有三道因式分解...火烧眉毛啊.1.X^3+6X^2+11X+62.X^4+X^2+2AX+1-A^23.X^4+2X^3+3X^2+2X+1要过程...

Question

有三道因式分解...火烧眉毛啊.
1.X^3+6X^2+11X+6
2.X^4+X^2+2AX+1-A^2
3.X^4+2X^3+3X^2+2X+1
要过程...

Answer 1

1.X^3+6X^2+11X+6
=(X^3+1)+(6X^2+11X+5)
=(X+1)(X^2-X+1)+(6X+5)(X+1)
=(X+1)(X^2-X+1+6X+5)
=(X+1)(X^2+5X+6)
=(X+1)(X+2)(X+3)
2.X^4+X^2+2AX+1-A^2
=(X^4+2X^2+1)-(X^2-2AX+A^2)
=(X^2+1)^2-(X-A)^2
=(X^2+1+X-A)(X^2+1-X+A)
3.X^4+2X^3+3X^2+2X+1
=(X^4+2X^2+1)+(X^3+X)+(X^3+X^2+X)
=(X^2+1)^2+X(X^2+1)+X(X^2+X+1)
=(X^2+1)(X^2+1+X)+X(X^2+X+1)
=(X^2+1+X)(X^2+X+1)
=(X^2+X+1)^2